The drone movie “Eye in the Sky” wants to make you think. Not in that way. It may open with an Aeschylus quote, but it’s only periodically pompous and only rarely about merely flattering preconceived notions, be they anti- or pro-. It’s far more interested in genuinely raising genuine questions about this new breed of warfare. Of the rash of recent drone movies (“Good Kill,” “Drones”), it’s the one most open to the idea that they might not be the devil — that they can lessen collateral damage and increase precision, even as they create a new hornet’s nest of problems. It even functions as a real-time nerve-jangler that only sometimes fumbles to make its points.

Jumping between the ground and various antiseptic rooms, “Eye in the Sky” presents modern warfare as a series of heated discussions across continents via conference calls and high-speed bandwidth. There’s a trigger-happy colonel (Helen Mirren) in a war room, plus a grouchy lieutenant-general (Alan Rickman) impatiently arguing with ministers over legality. Meanwhile in Las Vegas, two nervous pilots (Aaron Paul and Phoebe Fox) sit behind video game-like screens, awaiting orders they hope won’t come — even before a conveniently oblivious little girl appears, hawking bread right outside the strike zone.

Attempts to save her — or, failing that, fudge the intel so they won’t be tried for war crimes later — take up the bulk of “Eye in the Sky.” It plays like a calmer “Bourne” movie, with usually wan director Gavin Hood (“Tsotsi,” “X-Men Origins: Wolverine”) finding a cucumber cool approach as he jumps between various locations and endless tete-a-tetes. He creates a war film in which info is always accessible and shareable, with scarily accurate face-scanning programs and a contact on the ground (“Captain Phillips”’ charismatic Barkhad Abdi) who controls robot insects and birds fitted with micro-cameras. None of the tech makes the decisions any easier, and this very serious movie can still show it has a kicking sense of humor whenever some flustered official passes the buck to someone else.

At times it seems “Eye in the Sky” might have worked better as “Dr. Strangelove”-ian satire. Rickman, in his final in-the-flesh screen performance, slips in some Rickman-y discontent, and even scores a yuk early on when he buys the wrong doll for his young daughter. (His death makes his weary crack “Apparently there’s an important difference” even more devastatingly hilarious than it would be normally. Cherish these last blasts of his molasses drawl.)

“Eye in the Sky” could use more moments like that, though it can reveal humanity in unexpected places. We expect to sympathize with the doves manning the drones, but its hawk characters can surprise us, too, though only eventually. Mirren and Rickman spend most of the movie playing tetchy monsters who think of innocents as statistics, only to conveniently surprise us in the final stretch with sudden depths of feeling, even trauma. They still manage to complicate an issue drama that could have easily teemed with righteous speeches. Instead, it’s a conversation starter and a sound one, though don’t be surprised if you wind up debating why it included an unsubtle “irony” in which Rickman frets over buying his daughter a gift while arguing why they shouldn’t worry about bombing a cute little Kenyan girl.